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Rayleigh-Taylor finger instability mixing in hydrodynamic shell convection models

Mixing processes in stars driven by composition gradients as a result of the Rayleigh-Taylor instability are not anticipated. They are supported only by hydrodynamic studies of stellar convection. We find that such mixing occurs below the bottom edge of convection zones in our multidimensional hydrodynamic shell convection models. It operates at interfaces created by off-center nuclear burning, where less dense gas with higher mean molecular weight is located above denser gas with a lower mean molecular weight. We discuss the mixing under various conditions with hydrodynamic convection models based on stellar evolutionary calculations of the core helium flash in a 1.25 Msun star, the core carbon flash in a 9.3 Msun star, and of oxygen burning shell in a star with a mass of 23 Msun. We simulate the hydrodynamic behavior of shell convection during various phases of stellar evolution with the Eulerian hydrodynamics code HERAKLES in two and three spatial dimensions. Initial models for this purpose are obtained by state-of-the-art stellar evolutionary codes, namely GARSTEC, STAREVOL, and TYCHO for the core helium flash, core carbon flash, and oxygen shell burning, respectively. Most of our analysis is performed for two-dimensional hydrodynamic models of shell convection during the core helium flash at its peak covering approximately 250 convective turnover timescales. The mixing manifests itself in the form of overdense and cold fingers enriched with matter of higher mean molecular weight, originating from density fluctuations at the lower boundary of the convective shell, and "shooting" down into the core. They result from the Rayleigh-Taylor instability at the lower convection zone boundary due to a negative mean molecular weight gradient. They do not appear when the mean molecular weight gradient is positive.